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The Gamow-Teller strength distribution of the decay of $^{186}$Hg into$^{186}$Au has been determined for the first time using the total absorptiongamma spectroscopy technique and has been compared with theoretical QRPAcalculations using the SLy4 Skyrme force. The measured Gamow-Teller strengthdistribution and the half-life are described by mixing oblate and prolateconfigurations independently in the parent and daughter nuclei. The bestdescription of the experimental beta strength is obtained with dominantlyprolate components for both parent $^{186}$Hg and daughter $^{186}$Au. Theapproach also allowed us to determine an upper limit of the oblate component inthe parent state. The complexity of the analysis required the development of anew approach in the analysis of the X-ray gated total absorption spectrum.

On the $\beta$-decay of $^{186}$Hg